Q-motives and modular forms

A Q-curve is an elliptic curve E over which is isogenous to all its Galois conjugates. Serre's conjecture implies that Q-curves are modular. This means that E is a -simple factor of J1(N) for some level N. In this paper we will introduce Q-motives which are generalizations of Q-curves and present basic properties of Q-motives. Their properties are proved under some standard conjectures for motives.